Eighteen papers, many drawing from shows on the September 2001 convention in Genova, hide a variety of algebraic geometry. specific cognizance is paid to raised dimensional kinds, the minimum version software, and surfaces of the overall kind. an inventory of Francia's guides is integrated. participants comprise mathematicians from Europe, the U.S., Japan, and Brazil

This ebook presents a complete account of the speculation of moduli areas of elliptic curves (over integer earrings) and its software to modular kinds. the development of Galois representations, which play a primary position in Wiles' facts of the Shimura-Taniyama conjecture, is given. moreover, the ebook provides an summary of the facts of numerous modularity result of two-dimensional Galois representations (including that of Wiles), in addition to a few of the author's new ends up in that course.

This publication relies on one-semester classes given at Harvard in 1984, at Brown in 1985, and at Harvard in 1988. it truly is meant to be, because the identify indicates, a primary creation to the topic. having said that, a number of phrases are so as concerning the reasons of the ebook. Algebraic geometry has built drastically over the past century.

Fractals are a huge subject in such diverse branches of technology as arithmetic, computing device technological know-how, and physics. Classics on Fractals collects for the 1st time the ancient papers on fractal geometry, facing such subject matters as non-differentiable services, self-similarity, and fractional measurement.